Which European towns or cities are architecturally most similar today to how they would have been in the 16th and 17th centuries? A different way of asking the question: which contemporary European towns or cities would give the best impression of what a city would have looked like at that time?
There are many more authentic places in Europe. Cursory googling for things like "medieval town Europe" yields plenty of other examples.
Which towns or cities can one visit to experience this sense of space?
There are far too many to enumerate. Plenty of otherwise modern cities have an old district full of narrow streets and old buildings - including in cities that were mostly destroyed in WW2.
Here's Rue aux Fromages in Caen (France), as an example:
Here's another such street in Eger (Hungary), whose center is occasionally called "the Baroque Pearl of Europe":
But, again, the above are mere examples. Similarly authentic sites are all over the place in Europe if you care to search for them.